A Comparative Study of Storage Batteries for Electrical Energy Produced by Photovoltaic Panels

Abstract

This article presents a comparative study of the storage of energy produced by photovoltaic panels by means of two types of batteries: Lead–Acid and Lithium-Ion batteries. The work involved the construction of a model in MATLAB-Simulink for controlling the loading/unloading of storage batteries with energy produced by photovoltaic panels through a buck-type DC-DC convertor, controlled by means of the MPPT algorithm implemented through the method of incremental conductance based on a MATLAB function. The program for the MATLAB function was developed by the author in the C++ programming environment. The MPPT algorithm provides maximum energy transfer from the photovoltaic panels to the battery. The electric power taken over at a certain moment by Lithium-Ion batteries in photovoltaic panels is higher than the electric power taken over by Lead–Acid batteries. Two types of batteries were successively used in this model: Lead–Acid and Lithium-Ion batteries. Based on the results being obtained and presented in this work it may be affirmed that the storage battery Lithium-Ion is more performant than the Lead-Acid storage battery. At the Laboratory of Electrical Machinery and Drives of the Engineering Faculty of Bacau, an experimental stand was built for a storing system for electric energy produced by photovoltaic panels. For controlling DC-DC buck-type convertors, a program was developed in the programming environment Arduino IDE for implementing the MPPT algorithm for incremental conductance. The simulation part of this program is similar to that of the program developed in C++. Through conducting experiments, it was observed that, during battery charging, along with an increase in the charging voltage, an increase in the filling factor of the PWM signal controlling the buck DC-DC convertor also occurred. The findings of this study may be applicable to the storage of battery-generated electrical energy used for supplying electrical motors in electric cars.

1. Introduction

When considering potential applications of solar energy, both its advantages and disadvantages must be taken into account. The main advantages of solar energy are that it is non-polluting, it has a limitless supply as it is available everywhere, and it is free. Its main disadvantage is that since the solar radiation incident to the Earth surface is variable—being dependent on the day/night cycle, meteorological conditions, and the cycle of seasons—solar energy is dispersed across the globe. Because of this disadvantage, a need has arisen for the installation of solar energy storage equipment within energy systems. Research activity in this domain is currently focused on designing and building high-performing equipment for the storage of solar energy produced by photovoltaic systems. This work presents a comparative analysis concerning the control of batteries used for storing such energy. The main contributions of this study are as follows: the development of an innovative model, in the programming environment MATLAB-Simulink (version R2018a), of a system for storing electrical energy supplied by photovoltaic systems; the development of the MPPT algorithm of incremental conductance for controlling a buck DC-DC convertor; the elaboration of a control diagram for an electronic power circuit equipped with IGBT-type transistors for controlling the charging and discharging of batteries storing electrical energy; a comparative analysis of simulation results obtained for two types of batteries; and the construction of an experimental stand for controlling the charging of the batteries supplied by the photovoltaic panels by means of the buck DC-DC convertor. Measurements were taken from the MATLAB-Simulink model. The MPPT algorithm for controlling the buck DC-DC convertor based on the method of incremental conductance was implemented in the model through a MATLAB function, which the author developed in C++. In experiments, the MPPT algorithm for incremental conductance was implemented with the help of a program developed by the author in the programming environment Arduino IDE, which is similar to the program developed in C++.

Literature Review

Ref. [1] presents a solar panel connected to a mains supply through an energy storage system involving batteries. In this case, a system of photovoltaic panels generates the energy needed for supplying local consumers, and surplus energy is stored in batteries for further use. An autonomous hub for co-generating energy is presented in ref. [2]. A new topology for a step-up/step-down convertor is presented in ref. [3]. This system can adjust the output voltage’s average value by considering an input voltage fluctuating to the desired value of the reference rate. By means of this type of convertor, Lithium-Ion batteries can be charged by photovoltaic panels. Ref. [4] presents a prototype composed of a 3 kW supply source that simulates the running of solar panels, an electric battery, and an inverter. The prototype allows the charging and discharging cycles of the battery to be evaluated in order to establish the efficiency of electrical energy production by the photovoltaic panels. A comparative analysis of different energy storage methods for complex energetic systems is provided in ref. [5]. The most productive storage methods for complex energetic systems are exemplified in the storage systems of pumped hydroelectric energy, hydrogen systems, and thermal and thermochemical accumulations. In ref. [6], solar panels are used to charge the battery of a hybrid vehicle. As such, in addition to other energy sources, the photovoltaic panels contribute to enhancing the efficiency of the vehicle compared to a vehicle based only on a thermal engine. Ref. [7] presents an economic analysis of photovoltaic systems combined with electrical energy storage systems, revealing an important increase in the self-consumption of electrical energy. As such, the results prove that photovoltaic panels with energy storage systems are more advantageous than those without electrical energy storage systems. Ref. [8] presents an analysis of the most important applications in the electrical energy market where the storage of electrical energy confers several benefits: control over voltage and frequency, spare energy sources, load modeling and leveling, etc. Through a normalization technique based on five functions and a comparative evaluation, 19 electrical energy storage technologies are identified along the energetic chain. For low-scale residential applications, Pb–Acid and Li-Ion batteries are the most efficient, whilst for medium- and large-scale residential applications, as well as for industrial and commercial consumers, advanced Pb–Acid and melted-salt batteries are the most suitable. In ref. [9], a method is presented for calculating the maximum theoretical solar energy storage requirement in order to obtain an independent energy system. This method was applied in Taiwan to assess the annual energy storage requirements up until the year 2030 elaborated in the governmental plan. Refs. [4,10,11] present the usage of the photovoltaic panels for producing electrical energy in combination with the usage of thermal solar panels for supplying energy to residential habitations. These hybrid systems are controlled through various methods and allow the storage of both electrical and thermal energy. Analyses of energy management strategies developed for the systems based on photovoltaic batteries are presented in refs. [12,13]. The simulation and optimization of a photovoltaic system connected with Li-Ion batteries is presented in ref. [14]. Ref. [15] demonstrates how electrical energy produced by photovoltaic panels can be utilized to supply water pumping systems. Solar panels can also be used to charge batteries that supply electric vehicles. Refs. [16,17,18,19,20] present chargers for electric vehicle batteries based on photovoltaic solar panels. Such chargers can be implemented using convertors equipped with IGBT-type CMOS power transistors. Ref. [21] presents an innovative integrated PV-ESS (photovoltaic panel energy storage system) to enhance the speed of charging of an electric vehicle. This system redirects excess solar energy to an energy storage system. The stored energy is then efficiently used during the charging of the electric vehicle, thus diminishing dependence on the mains supply to a minimum. In ref. [22], a PI regulator with a fuzzy logic controller is presented for charging batteries using photovoltaic panels. In [23], modern technologies for manufacturing transparent, bi-facial, and flexible photovoltaic panels are presented. These technologies are aimed at improving the energy efficiency of the photovoltaic panels. Ref. [24] explores the connection between individuals who have photovoltaic panels and the probability of them owning a battery-powered electric vehicle. It was found that the probability of a household/family owning an electrical vehicle is significantly increased if the respective house is equipped with photovoltaic panels. Ref. [25] presents an analysis of the charging capacity of LiFeP04 batteries for use in electric vehicles with BLDC-type DC motors. In the abovementioned articles, a variety of applications for electrical energy produced by photovoltaic panels are presented, including its storage in batteries, its use to supply water pumping systems, and its delivery to the electrical grid. By optimizing photovoltaic systems connected with batteries, an increase in the quantity of energy produced by such systems can be achieved, leading to a reduction in the extent of environmental pollution. Research concerning the storage of electrical energy produced by photovoltaic panels requires practical implementation. This article presents a program, developed by the author in MATLAB-Simulink, for controlling the storage in batteries of electrical energy produced by photovoltaic panels.

2. Materials and Methods

2.1. Model in MATLAB–Simulink for Controlling Electric Energy Storage in Batteries

2.1.1. Description of Model Developed in MATLAB-Simulink Programming Environment

A diagram of the model developed in the MATLAB–Simulink programming environment for controlling energy storage in batteries is presented in Figure 1 below.

This model is composed of the following components: a photovoltaic module; a DC-DC step-down buck-type convertor; a control subsystem for the buck convertor based on the MPPT algorithm for incremental conductance; a power electronic circuit for controlling battery charging and discharging; a control block of transistors for the power electronic circuit; a measuring block for the parameters of the photovoltaic panels; and a measuring block for the parameters of the battery for storing the electrical energy produced by the photovoltaic panels. The photovoltaic module is composed of two photovoltaic panels connected in parallel, of the type Soltech 1STH-230P. The technical characteristics of the photovoltaic panel are $P_{max}=228.73$W and $U_{max}=37.1$V. From Figure 2, the values of the photovoltaic system at the maximum power point for an incident solar radiation intensity of 1000 W/m² at a temperature of 25 °C can be deduced as follows: $U_{max}=29.9$V, $P_{max}=457.5$W. The parameters of the buck-type DC-DC convertor are presented in ref. [26]. For the control of the photovoltaic panels, a diagram of the variation in solar radiation intensity during a time interval of 40 s is presented in Figure 3. The environment in which the photovoltaic panels were running was kept at a constant temperature of 25 °C. The values of solar radiation go in an upward direction and then in a downward direction, representing the battery’s discharging and charging modes.

A diagram of the control subsystem of the DC-DC buck-type convertor based on the MPPT algorithm for incremental conductance is illustrated in Figure 4. The power electronic circuit for controlling the battery’s charging and discharging modes is composed of two IGBT-type field-effect power transistors. This circuit is connected to the output terminals of the DC-DC buck-type convertor by means of an RC series-type filter circuit. The control block of the transistors is presented in Figure 1. It is composed of two proportional–integrative-type (PI_b and PI_b1) controllers and a signal-generating block, PWM. The measurement blocks for the photovoltaic panel parameters and battery parameters are represented in Figure 1 by the oscilloscopes PV1 and PV2.

For the photovoltaic panels, the oscilloscope PV1 measures their voltage variation, as well as the variation in their current intensity and electric power as a function of the variation in solar radiation during a time interval of 40 s. Meanwhile, the oscilloscope PV2 measures the charging status of the battery (SOC), as well as the variation in its current intensity and voltage as a function of the variation in solar radiation during a time interval of 40 s.

2.1.2. Functioning of Model Developed in MATLAB-Simulink

The electric energy produced by the photovoltaic panels is controlled using a step-down buck-type DC-DC convertor. The MPPT algorithm for incremental conductance is implemented in the control subsystem of the convertor as per Figure 4, with the help of a MATLAB function. In order to implement this algorithm, the author developed a program in the C++ programming language. The MPPT algorithm enables maximal transfer of energy from the photovoltaic panels to the battery. The design of the relations of DC-DC buck-type convertor elements is detailed in ref. [26]. The output of the buck convertor is connected to the storage battery by means of a power electronic circuit built with two IGBT-type transistors. Between the buck convertor and the power electronic circuit, a filter is inserted, based on an RC series circuit. The battery is connected to the two transistors, between the mass and the middle point of the circuit, by means of a group of resistors and inductors connected in series (RL). The transistor that receives the PWM control pulses of the type s_P will command the battery charging mode, whilst the transistor that receives the PWM control pulses of the type s_N will command the battery discharging mode. The two PWM signals of types s_P and s_N are interlocked in the control block of the battery through the module NOT. The error signal between the reference voltage value, equal to 24 V, and the voltage measured at the output of the buck convertor, V_bus, is processed through the discrete regulator PI_b1, which supplies the reference signal, Ib_ref, to the current regulator of the battery, PI_b. The current regulator, PI_b, processes the error signal between the reference value, Ib_ref, and the value of the current in the battery, Ib, in accordance with the adjustment law, PI, and provides, at the output, the control signal Duty_B for controlling the PWM signal generator block. The PWM signals at the output of the generator block (PWM Generator) are transmitted to the two transistors in the power electronic circuit. Variations in the photovoltaic panel parameters and battery parameters are measured with the help of oscilloscopes PV1 and PV2. The types and parameters of the batteries used in this model are presented in Figure 5.

In this model, two types of batteries are used: Lead–Acid and Lithium-Ion batteries. The parameters of these batteries are as follows: rated voltage = 12 V; rated capacity = 100 Ah; initial charging status = 45%; response time of battery = 1 s.

3. Simulation Results

The model developed in MATLAB Simulink was employed to simulate the functioning of each battery type without modifying any other structural parameters. The variations in the photovoltaic panel parameters were identical for both battery types, and are presented in Figure 6. The electric power supplied by the photovoltaic panels is modified as a function of the variation in solar radiation intensity. Under a solar radiation intensity of 1000 W/m², the photovoltaic panels will produce 0.3 kW of electrical power. The variations in the Lead–Acid battery parameters as a function of the variation in solar radiation intensity are presented in Figure 7, and the variations in the Lithium-Ion battery parameters as a function of the variation in solar radiation intensity are presented in Figure 8.

Comparative Analysis of Simulation Results

The variation in solar intensity as a function of time is shown in Figure 3, and remains the same for both storage batteries. The values of the Lead–Acid and Lithium-Ion battery parameters were determined by means of digital measuring instruments inserted into the model, as per Figure 1. The simulation program was launched by pushing the button Run on the control bar of the model (see Figure 1). The instruments for measuring the battery’s charging capacity, SOC, the current intensity in the battery, Ib, and the voltage at the battery terminals, Ub, were set to display the measured values in long format (with more decimals) to make the values more easily readable. To read the battery parameters, the performance of the simulation was interrupted by pushing the Run button. For practical purposes, a pause was added in the running of the simulation program. After reading the battery parameter values, the Run button was pushed again and the simulation was resumed. Each interruption of the simulation program proceeded in the same manner. The simulation program was launched for each type of battery for storing electrical energy. The obtained parameter values for the Lead–Acid and Lithium-Ion batteries as a function of the time elapsed since the program was launched are presented in

Table 1. Values of electrical energy storage battery parameters.

Time	SOC		Ib		Ub
	Battery (Lead–Acid)	Battery (Lithium-Ion)	Battery (Lead–Acid)	Battery (Lithium-Ion)	Battery (Lead–Acid)	Battery (Lithium-Ion)
0	44.999	44.999	3.335	3.08	11.846	12.898
4	44.996	44.996	3.01	3	11.843	12.897
8	44.996	44.995	−3.069	−2.961	11.897	12.914
12	44.998	44.998	−3.163	−3.08	11.92	12.914
16	45.002	45.002	−2.914	−2.957	11.943	12.914
20	45.005	45.005	−2.999	−2.883	11.967	12.914
24	45.008	45.008	−1.563	−1.409	11.98	12.911
28	45.009	45.009	−1.361	−1.12	11.984	12.909
32	45.01	45.01	0.007	0.008	11.983	12.906
36	45.01	45.01	0.007	0.008	11.982	12.906
40	45.009	45.01	3.022	3.032	11.958	12.9

.

Based on the values of the electric energy storage battery parameters, the diagram shown in Figure 9 was drawn. The parameters shown in this diagram are as follows: SOC_LA—the charging status of the Lead–Acid battery; SOC_Lt_I—the charging status of the Lithium-Ion battery; Ib_LA—the current intensity of the Lead–Acid battery; Ib_Lt-I—the current intensity of the Lithium-Ion battery; Ub_LA—the voltage at the terminals of the Lead–Acid battery; and Ub_Lt-I—the voltage at the terminals of the Lithium-Ion battery.

The measurement units for the values presented on the y axis in Figure 8 are as follows: the loading status of the battery SOC is measured in %; the current intensity in the battery, Ib, is measured in A; and the voltage at the terminals of the battery, Ub, is measured in V. The analysis of the results presented in Table 1, the diagram in Figure 9, and the characteristics of variation in the battery parameters shown in Figure 7 and Figure 8 leads to the following conclusions: the values obtained for each battery’s charging status (SOC) are practically equal, while the current intensity of the Lead–Acid battery is a little higher than that of the Lithium-Ion battery. When the batteries are discharged, the current intensities of both batteries have positive values, and when batteries are charged, their current intensities have negative values. In this study, a receptor circuit was not connected to the battery. Battery discharge occurs when the intensity of solar radiation decreases and the photovoltaic panels cannot supply the electrical power needed in order to charge the battery. At t = 20 s, the current intensity of the Lead–Acid battery is Ib_LA = −2.999 A, and the current intensity of the Lithium-Ion battery is Ib_Lt-I = −2.883 A. Furthermore, the voltage at the Lead–Acid battery terminals is lower than the voltage at the Lithium-Ion battery terminals: at t = 20 s, the voltage of the Lead–Acid battery is Ub_LA = 11.967 V, and the voltage of the Lithium-Ion battery is Ub_Lt-I = 12.914 V. In addition, the electric power of the Lead–Acid battery at t = 20 s is 35.88 W, and the electric power of the Lithium-Ion battery is 37.23 W. Based on these values, it can be concluded that the Lithium-Ion storage battery exhibits higher performance than the Lead–Acid storage battery, because it is charged with a higher electrical power.

4. Building the Experimental Stand

A picture of the experimental stand is presented in Figure 10. This stand is composed of the following: 1—Arduino Uno development board; 2—ACS 712 current sensor; 3—buck-type DC-DC convertor; 4—adjustable current-controlled voltage source; 5—ammeter; 6—voltmeter; 7—batteries; 8—laptop. To control the battery charge, a program was developed based on the MPPT algorithm for incremental conductance. The ACS 712 current sensor can measure currents of up to 20 A and has a sensitivity of 0.1 V/A. It supplies a voltage signal to the A2 channel of the Arduino Uno development board. The characteristics and running mode of the DC-DC buck-type convertor have been presented in ref. [26]. In ref. [26], a calculation method for the signal supplied by the ACS 712 current sensor is presented, as well as a calculation method for the signal supplied by the voltage sensor composed of a resistive divider, R1–R2. In ref. [26], a buck-type DC-DC convertor was used to supply a resistive load. In the current study, the same buck DC-DC convertor was used, but instead of a resistive load, batteries were connected. The electrical setup of this convertor also included a voltage divider made from resistors to measure the voltage of the convertor input. The current-controlled voltage source had the following features: an adjustable voltage range of (0–30) V D.C. and a range of (0–5) A for the variation in the current as a function of the load connected to the source terminals. This source was used in the laboratory instead of photovoltaic panels. The ammeter used was an analog instrument that measured the current intensity of the battery charging within a measuring range of 0 to 5 A. The voltmeter used was a digital instrument that could measure voltage rates within the range of (0–200) V D.C. The batteries used were acid-type batteries with a charging capacity of 80 Ah each. Two 12 V D.C. car batteries, connected in series, were used because the buck-type DC-DC convertor was designed and built to produce an output voltage of 24 V D.C. The batteries were connected to the voltage source by means of the buck-type DC-DC convertor. After connecting the adjustable voltage source to the input of the DC-DC buck-type convertor, and connecting the batteries to the convertor output, the following measurements were taken within one charging cycle of the batteries (as per

Table 2. Experimental determinations.

Time	Usource	Isource	Ibattery	Ubattery	PWM Factor
12.25	26.1	0.98	1.32	22.95	130
12.30	26.1	1.07	1.37	23.12	146
12.35	26.1	1.20	1.47	23.27	157
12.40	26.1	1.28	1.57	23.30	161
12.45	26.0	1.37	1.65	23.38	176
12.50	26.0	1.48	1.70	23.46	188

):

The experimental stand simulated a storage system for electrical energy produced by photovoltaic panels. By means of the algorithm for incremental conductance, the maximum required power for charging the batteries was supplied. Analysis of the experimental results revealed that during battery charging, along with an increase in the charging voltage, an increase in the filling factor of the PWM signal that controls the DC-DC buck convertor also takes place, as per Figure 11. In the future, more studies on Lithium-Ion batteries will be conducted.

5. Conclusions

This work presents a comparative analysis of a system for controlling batteries used for storing electrical energy produced by photovoltaic systems. The implementation of this system involved the development of a model in MATLAB-Simulink for controlling the loading/unloading of storage batteries with energy produced by photovoltaic panels using a buck-type DC-DC convertor controlled by means of the MPPT algorithm, which was implemented through the method of incremental conductance based on a MATLAB function. The program for the MATLAB function was developed by the author in the C++ programming environment. The MPPT algorithm provided maximal transfer of energy from the photovoltaic panels to the battery. Between the buck-type DC-DC convertor and the battery, a power electronic circuit made of IGBT-type transistors was inserted. This circuit allowed for control over battery charging and discharging. The transistors were controlled using a voltage controller and a current controller of the proportional–integrative (PI) type. In this manner, control over the voltage and current intensity was assured for the battery during its charging and discharging processes. In this study, a receptor circuit was not connected to the battery. Practically, battery discharge occurs when the solar radiation intensity is low and the photovoltaic panels cannot supply the power needed to charge the battery. During discharging, the current intensity value is positive, whilst during charging, the current value in the battery is negative. In this model, two types of batteries were successively used: Lead–Acid and Lithium-Ion batteries. The analysis of the results presented in Subchapter 3 shows that the current intensity of the Lead–Acid battery was a little higher than that of the Lithium-Ion battery. Within a time interval of 40 s, at t = 20 s, the current intensity of the Lead–Acid battery was Ib_LA = −2.999 A, and that the Lithium-Ion battery was Ib_Lt-I = −2.883 A. At the same time point, the voltage rate of the Lead–Acid battery was lower than that of the Lithium-Ion battery. At t = 20 s, the voltage of the Lead–Acid battery was Ub_LA = 11.967 V, and that of the Lithium-Ion battery was Ub_Lt-I = 12.914 V. Based on these results, it can be concluded that Lithium-Ion storage batteries exhibit higher performance than Lead–Acid storage batteries, because they are charged with a higher electric power. At the Laboratory of Electrical Machinery and Drives of the Engineering Faculty in Bacau, an experimental stand was built for a storage system for electrical energy produced by photovoltaic panels. To control the buck-type DC-DC convertor, a program was developed in the programming environment Arduino IDE in order to implement the MPPT algorithm for incremental conductance. During the experimental tests, it was also observed that during battery charging, an increase in the filling factor of the PWM control signal of the DC-DC buck-type convertor took place. The findings of this study may also be applicable to electrical energy storage batteries used for supplying electrical motors in electric vehicles.